document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173693>Question 173693</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh>Algebra Structure and Method Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I would appreciate your help on the following problem:  The two digits in the numerator of a fraction whose value is 4/7 are reversed in its demoninator.  The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original demonimator.  Find the original fraction.  I have 10t+u/10u+t=4/7; 10u+t/10t+u=10t+u+16/10u+t-5.<BR>\n" );
document.write( "7(10t+u)=4(10u+t), 70t+7u=40u+4t, 66t=33u, t=3/6u.  I'm not sure where to go from there.  Thank you so much for any help you can give me.  I appreciate it so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128581 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I follow what you were trying to do, but I think you made this too difficult on yourself.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810t%2Bu%29%2F%2810u%2Bt%29=4%2F7 ALIGN=MIDDLE  ALT=\"%2810t%2Bu%29%2F%2810u%2Bt%29=4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is spot on.\r<BR>\n" );
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document.write( "But if the value of the original fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the value of the original fraction's reciprocal must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F4 ALIGN=MIDDLE  ALT=\"7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so for the second relationship I think you should use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810t%2Bu%2B16%29%2F%2810u%2Bt-5%29=7%2F4 ALIGN=MIDDLE  ALT=\"%2810t%2Bu%2B16%29%2F%2810u%2Bt-5%29=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cross-multiplying and collecting like terms until the equations are in standard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy=C ALIGN=MIDDLE  ALT=\"Ax%2BBy=C\"   DISABLED_style= \"max-width:90%; height:auto;\" > form, you should have the following:\r<BR>\n" );
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document.write( "Eq. 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66t-33u=0 ALIGN=MIDDLE  ALT=\"66t-33u=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and Eq. 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33t-66u=-99 ALIGN=MIDDLE  ALT=\"33t-66u=-99\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply Eq. 1 by -2:  Eq. 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-132t%2B66u=0 ALIGN=MIDDLE  ALT=\"-132t%2B66u=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add Eq. 3 to Eq. 2:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-99t=-99 ALIGN=MIDDLE  ALT=\"-99t=-99\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594;  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute into Eq. 1:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%281%29-33u=0 ALIGN=MIDDLE  ALT=\"66%281%29-33u=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33u=66 ALIGN=MIDDLE  ALT=\"33u=66\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=2 ALIGN=MIDDLE  ALT=\"u=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the original fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F21 ALIGN=MIDDLE  ALT=\"12%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > which has a value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and further, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2B16%29%2F%2821-5%29=28%2F16=7%2F4 ALIGN=MIDDLE  ALT=\"%2812%2B16%29%2F%2821-5%29=28%2F16=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer checks.\r<BR>\n" );
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